Question

Draw a labeled diagram of Van de Graff generator. State its working principle to show how by introducing a small charged sphere into a larger sphere, a large amount of charge can be transferred to the outer sphere. State the use of this machine and also point out its limitations.

Answer 1

Van de graff generator is a device used for building up a high potential difference of the order of a few million volts. It is based on the principle that the charge on a conductor is moved to the outer surface and distributed uniformly over it.

Limitation of van de graff generator are as follows :

1. It is a series of combinations that allow one direction for movement of charge.

2. It can accelerate only the charged particles.

Let the inner sphere of radius r carry a charge of q and the outer sphere of radius R carry a charge of Q.

Then potential on surface of smaller sphere due to both the charges is:

$V\left(r\right)=\frac{1}{4\pi {\epsilon }_o}(\frac{Q}{R}+\frac{q}{r})$

Then potential on surface of larger sphere due to both the charges is:

$V\left(R\right)=\frac{1}{4\pi {\epsilon }_o}(\frac{Q}{R}+\frac{q}{R})$

$V\left(r\right)-V\left(R\right)=\frac{q}{4\pi {\epsilon }_o}(\frac{1}{r}-\frac{1}{R})$

This means that inner sphere always remains at a higher potential. Now, connecting the two spheres will allow charge flow from the inner sphere to the outer sphere irrespective of the amount of charge on the outer sphere. This allows a large accumulation of charge on the outer sphere.

It is used for moving the belt to accumulate the electric charge on a hollow metal globe on the top of an insulated column. It is also used to generate or produce high voltage.

One of the limitations of Van de Graff generator is the potential to which the dome can be raised.